TY - GEN

T1 - Second-order linear-time computability with applications to computable analysis

AU - Kawamura, Akitoshi

AU - Steinberg, Florian

AU - Thies, Holger

N1 - Funding Information:
Acknowledgements. This work was supported by JSPS KAKENHI Grant Numbers JP18H03203 and JP18J10407, by the Japan Society for the Promotion of Science (JSPS), Core-to-Core Program (A. Advanced Research Networks), by the ANR project FastRelax (ANR-14-CE25-0018-01) of the French National Agency for Research and by EU-MSCA-RISE project 731143 “Computing with Infinite Data” (CID).

PY - 2019

Y1 - 2019

N2 - In this work we put forward a complexity class of type-two linear-time. For such a definition to be meaningful, a detailed protocol for the cost of interactions with functional inputs has to be fixed. This includes some design decisions the defined class is sensible to and we carefully discuss our choices and their implications. We further discuss some properties and examples of operators that are and are not computable in linear-time and nearly linear-time and some applications to computable analysis.

AB - In this work we put forward a complexity class of type-two linear-time. For such a definition to be meaningful, a detailed protocol for the cost of interactions with functional inputs has to be fixed. This includes some design decisions the defined class is sensible to and we carefully discuss our choices and their implications. We further discuss some properties and examples of operators that are and are not computable in linear-time and nearly linear-time and some applications to computable analysis.

UR - http://www.scopus.com/inward/record.url?scp=85064868996&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064868996&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-14812-6_21

DO - 10.1007/978-3-030-14812-6_21

M3 - Conference contribution

AN - SCOPUS:85064868996

SN - 9783030148119

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 337

EP - 358

BT - Theory and Applications of Models of Computation - 15th Annual Conference, TAMC 2019, Proceedings

A2 - Watada, Junzo

A2 - Gopal, T. V.

PB - Springer Verlag

T2 - 15th Annual Conference on Theory and Applications of Models of Computation, TAMC 2019

Y2 - 13 April 2019 through 16 April 2019

ER -